Question

Mary, who is sixteen year old is four times as old as her brother. How old will Mary be when she is twice as old as her brother?

Answer 1

Hint: The age word problems are one application of linear equations. What are termed as age problems when solving age problems, generally the age of two different people or objects both now and in the future or past are compared. The objective of these problems is usually to find each subject’s correct age. Since there can be a lot of information in these problems, a chart can be used to help organize and solve.
To solve the above given problem first we have to find the age of her brother when Mary is sixteen years old and to find that one condition is given. After finding that we will assume any \[x\] year when Mary will be twice as old as her brother from there we will get the value of \[x\] and also the age at Mary when she is twice as old as her brother.

Complete step by step solution:
Given that Mary is \[16\] years old and her brother is four times younger which means the age of her brother when she is \[16\] is \[4\].
Now,
i.e x be the year when Mary will be twice as old as her brother.
So the age at Mary in x years is \[16+x\]
and age of her brother in \[x\] years is \[4+x\]
So, the expression comes out will be
\[16+x=2\left( 4+x \right)\]
\[x=8\]
Now putting this value of \[x\] in the age of Mary
\[\therefore \] The Mary age will be
\[16+8=24\] years old.
While the age of her brother will be
\[4+8=12\] years old.

Note: When assuming the year when the age at Mary is twice the age of her brother the year will be counted from after the age at Mary means the value of \[x\] is the addition to the age of Mary and her brother.